TL;DR: In this article, the authors present a simple and easily calculated expression for the Shapley value whenever the characteristic function is a "cost" function with the property that the cost of any subset of players is equal to the "largest" player in that subset.
Abstract: We present a simple and easily calculated expression for the Shapley value whenever the characteristic function is a “cost” function with the property that the cost of any subset of players is equal to the cost of the “largest” player in that subset. It turns out that a simple rule previously proposed for calculating airport landing charges generates precisely the Shapley value for an appropriately defined game.
TL;DR: This work considers the major aspects of airport operational capacities relevant to the strategic management of air traffic, and the underlying mathematical model is presented, as well as numerical examples illustrating the benefits when solving airport congestion problems.
Abstract: A major goal of air traffic management is to strategically control the flow of traffic so that the demand at an airport meets but does not exceed the operational capacity. This work considers the major aspects of airport operational capacities relevant to the strategic management of air traffic. A representation of airport capacity that properly reflects an airport's operational limits is discussed. A method is presented for estimating practical airport capacities under various operational conditions. A technique is proposed for optimizing the available airport capacity to best satisfy the expected traffic demand. The optimization is achieved by considering arrival and departure operations as interdependent processes and by strategically allocating the airport capacity between arrivals and departures. The underlying mathematical model is presented, as well as numerical examples illustrating the benefits when solving airport congestion problems. >
TL;DR: In this article, the authors explore the implications of an alternative pricing philosophy where the common costs of runway construction are shared among the different aircraft types according to a club principle, and suggest new rules of thumb for allocating common costs based on the Shapley value and the nucleolus.
Abstract: Discussion of airport pricing policy has largely centered on the problem of congestion, but at most airports congestion is negligible. In the present paper we explore the implications of an alternative pricing philosophy where the common costs of runway construction are shared among the different aircraft types according to a club principle. Linear programming and game theory techniques are used to clarify the notions of optimal runway size and fair and efficient landing fees, and to suggest new rules of thumb for allocating common costs based on the Shapley value and the nucleolus. The model is applied to Birmingham Airport to assess investment and pricing policy in 1968-1969. To the authors' knowledge this paper is the first explicit application of the "club principle" and the largest numerical application of game theory to date.
TL;DR: A survey and critique of the literature on airport capacity can be found in this paper, where the authors describe how the capacity of a runway configuration depends upon the strategy for sequencing various types of operations (heavy or light arriving or departing aircraft), the runway geometry, the instrument flight rules, etc.
Abstract: The following is a survey and critique of the literature on airport capacity. It was originally written as a set of lecture notes for a university course on airport planning. The purpose is to describe, in as simple a way as possible, how the capacity of a runway configuration depends upon the strategy for sequencing various types of operations (heavy or light arriving or departing aircraft), the runway geometry, the instrument flight rules, etc.
TL;DR: The Taxi Planning has been modelled using a linear multicommodity flow network model with side constraints and binary variables to represent the conflicts and competence between aircrafts using a given airport capacity.
Abstract: The Taxi Planning studies the aircraft routing and scheduling on the airport ground. This is a dynamic problem, which must be updated almost every time that a new aircraft enters or exits the system. Taxi Planning has been modelled using a linear multicommodity flow network model with side constraints and binary variables. The flow capacity constraints are used to represent the conflicts and competence between aircrafts using a given airport capacity. The “Branch and Bound” and “Fix and Relax” methodologies have been used. The computational tests have been run at the Madrid-Barajas airport, using actual data from the airport traffic.